Trim the ends and any strings from the pea pods. If using fresh mushrooms, trim the stem ends and discard (or save for soup).
Slice the mushrooms into 1/2-inch-wide slices. If using dried mushrooms, put them in a bowl with enough cold water to cover. Place bowl in microwave, uncovered, and microwave on high for 1 minute.
Let the mushrooms sit in warm water until completely softened, about 30 minutes, then drain, squeeze out the liquid (save for soup), and cut off and discard the tough stems. Cut the caps into 1/2-inch-wide pieces.
Heat the oils in a skillet and add the mushrooms. Sauté over medium-high heat, stirring, until the mushrooms just begin to brown. Sprinkle the sugar over the mushrooms and add the wine and shoyu.
Cook and stir for 1 minute, and steam until the pea pods are just tender-crunchy and bright green, about 2 minutes. Remove cover and continue to cook, until most of the liquid is evaporated.
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